Method for improving the accuracy of rock property values derived from digital images

ABSTRACT

A method for increasing the accuracy of a target property value derived from a rock sample is described in which the sample is scanned to obtain a three-dimensional tomographic digital image which can be processed to pore space and solid material phases through a segmentation process. A process is used which revises the segmented volume, e.g., by increasing pore space connectivity, in a manner affecting the target property value that would be derived. Another described method increases the accuracy with which a segmented volume represents a material sample having structure not adequately resolved in an original three-dimensional tomographic digital image. Further, a system for performing the processes, and a segmented digital volume which more accurately represents a sample of a porous media, are described.

This application claims the benefit under 35 U.S.C. §119(e) of priorU.S. Provisional Patent Application No. 61/681,700, filed Aug. 10, 2012,which is incorporated in its entirety by reference herein.

BACKGROUND OF THE INVENTION

This invention relates to the field of digital imaging analysis and morespecifically to digital rock physics and methods for obtaining improvedvalues for rock properties derived from digital images.

Acquiring, developing and managing hydrocarbon reservoirs involve manydecisions that are sensitive to the quality of information about thephysical properties of the reservoir rock. For instance, accurateassessments of porosity, absolute permeability, relative permeability,capillary pressure, electrical resistivity, and elastic properties ofrock under investigation are each of interest and value to reservoirengineers in applications including well planning, completion design,and reservoir estimates. Detailed, specific information on rockstructure and properties can be useful on its own or can facilitateleveraging the greatest value out of logging and seismic data to whichit provides important context. Some of the traditional techniques toacquire information about the reservoir rock have determined propertiesby measuring overall effect, e.g., permeability might be establishedwith a permeameter forcing a fluid through a rock sample and recordingthe resulting fluid flux and pressure drops. However, such attempts toacquire information may be limited by the shape and size of the sampleand are often otherwise not well suited to providing quality informationin a timely manner.

Digital rock physics is an important tool for facilitating a better,quicker, and more efficient insight into rock structure and propertiesof interest. Such techniques produce values of important rock propertiesthrough analysis of three-dimensional (3D) images, also referred to asvolumes or digital objects, representing the natural rock samples.Original grey-scale image acquisition uses scanning operations such asX-Ray computed tomography scans (CT scans) or with a focused ion beamscanning electron microscope (FIB-SEM scanning). Such techniquesintegrate a succession of cross-sectional scans into a whole 3D image.This original grey-scale image can be processed with segmentationtechniques through subdividing the volume into discrete sub volumes,individual voxels at the most elementary level, and processing these toproduce segmented volumes with each voxel allocated to either pore or avariety of solid material phases. As used herein, “solid materialphases” means the mixture of grains of various minerals, cementationcomponents, and all else that is not pore space as imaged by the scan.

A variety of segmentation methods are known to those skilled in the artof digital rock physics. These segmentation methods include, forexample, those shown by Toelke, J., et al. (2010), “Computer simulationsof fluid flow in sediment: From images to permeability,” The LeadingEdge (January 2010), 68-74, (hereinafter, the “Toelke (2010)”publication), and U.S. Pat. No. 8,081,802 B2 to Dvorkin et al.(hereinafter, the '802 patent).

Values for important properties can be estimated, modeled, or simulatedwith the resulting segmented volumes. See, e.g., Dvorkin, J., et al.(2011), “Relevance of computation rock physics,” Geophysics, 76(5),E141-E153 (hereinafter, the “Dvorkin 2011” publication) and the '802patent.

Circumstances are sometimes encountered, however, in which the value ofone or more properties derived only from segmented volumes isunreliable. One such circumstance capable of producing unreliableproperty values occurs when important structure is below the resolutioncapabilities. These limitations may commonly be the result of the needto work with manageably sized data sets for computations and simulationsand in this case derive from the scanning resolution in combination withthe field-of-view required to address a representative sample.Alternatively, in some cases structural features contributing toproperties of interest may be too small to accurately capture in scannedimages as a limitation of the scanning equipment itself, such assub-resolution or under-resolved features. Either way, there areinstances in which an important structure is not directly captured,e.g., very thin conduits connecting the pores in some samples may notaccurately resolve even at the highest magnifications practicallypossible. This may result in a segmented volume which does notadequately represent the actual structure of the rock.

In such cases, usual analytical techniques deriving values from suchvolume can yield unreliable values, e.g., an absolute permeability k forthe rock that is unrealistically small or even at zero where the actualeffective characteristics for that rock are quite different, e.g.,production data proves otherwise. Values for elastic properties,relative permeability, capillary pressure, electrical resistivity, andother rock properties may be similarly affected. Greater accuracy forsuch values is important for decisions critical to determining whatreservoir zones are of commercial interest and how to develop a field.

These resolution issues have become a well-recognized challenge. Dvorkin(2011) discusses the problem (e.g., E144), as does Toelke (2010) in thediscussion of “unresolved pores” (p. 70) thereof, and Knackstedt, M. A.,et al. (2004), “Digital core laboratory: Properties of reservoir corederived from 3D images,” SPE Asian Pacific Conference on IntegratedModeling for Asset Management. SPE 87009, discusses the problem. It hasbeen proposed to address such sub-resolution and/or under-resolvedfeatures by adjusting the mathematical models that are used to deriveproperty values from the segmented volumes. See, e.g., Toelke (2010),and the published European Patent Application publication no. EP2090907A1 for a Method for determining the properties of hydrocarbonreservoirs from geophysical data, for discussions of adjusting themathematical models and/or changing values ascribed to phases. Theseadjustments are limited and can fail to produce digital volumes withstructural features representative of the rock under investigation.

The use of filters with the grey-scale image and a seeding/regiongrowing segmentation approach such as disclosed in the '802 patent canassist effective image processing by removing various anomalies andsmoothing data. However, images so addressed still fail to captureconnections between the pore spaces that account for properties presentbut which result from structure below the full resolution of thescanner.

A watershed transform had also been applied to further manipulatedigital volumes. See, generally, Vincent, L., et al. (1991), “Watershedin digital spaces: An efficient algorithm based on immersionsimulations,” IEEE Transactions on Pattern Analysis and MachineIntelligence. 13(6), 583-598 (hereinafter, the “Vincent (1991)”publication) and Faessel, M., et al., (2009), “Touching grain kernelsseparation by gap-filling,” Image Anal Stereol. 29. 195-203., whichintroduce application of the watershed transform and application to theinverse of the distance function and to gap-filling techniques. See,e.g., Sakellariou, A., et al. (2007), “Developing a virtual materialslaboratory,” Materials Today, 10(12), 44-51, which discusses usingwatershed to decompose an object. Quintal, B., et al. (2011),“Integrated numerical and laboratory rock physics applied to seismiccharacterization of reservoir rocks,” The Leading Edge, (December 2011),1360-1376 (hereinafter, the “Quintal (2011)” publication), relates tolocalizing the grain contacts below the data resolution, a“grain-contact reconstruction” method. However, the Quintal (2011)application of watershed produces unrealistic results due to “unresolvedmicrocracks and other microstructures, which cannot be detected with thegrain contact reconstruction technique” and then shows alteration of themathematical model to compensate.

As in other prior approaches, such compensation can facilitate producingan improved value, but does not correct the structure featured in thesegmented volume to best represent the rock sample.

Thus, the present investigators have recognized that there is a need fordeveloping a method for adjusting the segmented volume to effectivelyamend the structure featured therein to represent the rock sample morerealistically and thereby produce more reliable property values.

SUMMARY OF THE INVENTION

A feature of the present invention is a method for increasing theaccuracy of a target property value derived from a sample of a porousmedia with digital imaging techniques.

A further feature of the present invention is a method to provide amethod for revising or adjusting the representation of a segmentedvolume which corresponds to the sample under investigation to accountfor sub-resolution and/or under-resolved features, such as cracksproviding connectivity between pores space which can affect fluidtransport properties of the sample.

Another feature of the present invention is a segmented digital volumethat can more accurately represent a sample of a porous media.

To achieve these and other advantages and in accordance with thepurposes of the present invention, as embodied and broadly describedherein, the present invention relates, in part, to a method forincreasing the accuracy of a target property value derived from adigital image corresponding to a material sample, which comprises stepsa) to e). In step a), a three-dimensional tomographic digital image ofthe material sample is obtained. In step b), a preliminary segmentedvolume is generated which corresponds to the material sample byprocessing the three-dimensional tomographic digital image through asegmentation process. In step c), a criterion relation which is obtainedindependently of the preliminary segmented volume is defined as afunction of values of criterion properties related to the targetproperty. In step d), an adjusted segmented volume is created throughadditional processing revising features to the preliminary segmentedvolume, which comprises 1) applying a processing step to identifylocations for potentially revising features of the preliminary segmentedvolume, 2) applying revision features to the preliminary segmentedvolume to create a revised segmented volume; 3) deriving trial values ofcriteria properties from the revised segmented volume; 4) repeating atleast steps 2)-3) on the revised segmented volume until trial values ofcriterion properties satisfy the criterion relation. In step e), a finalvalue for the target property is derived from the adjusted segmentedvolume.

The present invention also relates to a method for increasing theaccuracy of a target property value derived from a digital imagerepresenting a porous material sample, which comprises steps of a)-e).In step a), a three-dimensional tomographic digital image comprising agrey-scale volume of the sample is obtained. In step b), a segmentedvolume is obtained that represents the sample by processing thegrey-scale volume to pore space and a plurality of solid material phasesthrough a segmentation process. In step c), a criterion relationshipwhich is developed independently of the segmented volume is obtained asa function of a pair of criterion properties related to the targetproperty. In step d), an adjusted segmented volume is created throughadditional processing, which comprises 1) determining where to add aplurality of cracks to the segmented volume, which comprises: i)creating an inverse distance map of the pore space to the solid materialphase boundaries in the segmented volume; ii) creating a watershedsurface identifying locations for potentially introducing cracks intothe solid material phases by applying a watershed processing step to theinverse distance map; and iii) selecting potential crack locations asall portions of the watershed surface located in the solid phases of thesegmented volume; 2) selecting a value for degree of volume revision; 3)producing a revised segmented volume, comprising: I) selecting a portionof potential crack locations guided by degree of revision value; II)converting the voxels of the segmented volume which are located on theselected portion of potential crack locations from solid phases to pore;4) deriving the values of criterion properties from the analysis of therevised segmented volume; 5) repeating at least the steps 3 through 4 byvarying the selected degree of volume revision until the values of thecriterion properties derived in step 4 satisfy the criterionrelationship; and 6) selecting the revised segmented volume whichproduced the set of criterion properties which satisfy the criterionrelationship best, as the adjusted segmented volume. In step e), theadjusted segmented volume is used to derive the target property value.

The present invention also relates to a method for increasing theaccuracy of a target property value derived from a digital imagerepresenting a rock sample, which comprises steps a)-f). In step a), agrey-scale digital volume of the rock sample is obtained. In step b), apreliminary segmented volume of the rock sample is obtained byprocessing the grey-scale volume to a plurality of pore spaces and atleast one solid material phase separated through a segmentation process.In step c), a criterion curve which is developed independently of thepreliminary segmented volume is defined as a function of a pair ofcriterion properties related to the target property. In step d), anadjusted segmented volume is created through additional processing,which comprises 1) determining where to add a plurality of cracks to thesegmented volume, which comprises i) creating an inverse distance map ofthe pore space to the solid material phase boundaries in the preliminarysegmented volume, ii) applying a processing step identifying locationsfor potentially introducing cracks into the solid material phase as afunction of the inverse distance map, and 2) introducing cracks to thepreliminary segmented volume until the adjusted segmented volumeassociated with values for the pair of criterion properties thatsatisfies the criterion curve to produce an adjusted segmented volume.In step e), an improved segmented volume which incorporates the cracksrealized in the identified adjusted segmented volume is produced andstored. In step f), the improved segmented volume is used to derive afinal value for the target property.

A method for developing an adjusted absolute permeability value from asegmented volume created from tomographic image data obtained at aresolution insufficient to effectively resolve pore space connectivitydirectly from a rock sample under investigation, wherein the methodcomprises steps a)-k). In step a), a segmented volume is obtained whichrepresents the rock sample segmented to pore spaces and solid materialphase, which comprises 1) scanning the rock sample to produce agrey-scale image; and 2) segmenting the grey-scale image to produce asegmented volume composed of voxels representing pore space and voxelsrepresenting at least one solid material phase. In step b), a grey-scalevalue is obtained which characterizes pore space. In step c), agrey-scale value is obtained characterizing solid material. In step d),a criterion curve which is developed independently of the segmentedvolume is defined as a function of a select elastic property andporosity. In step e), an inverse distance map of the pore space to thesolid material phase boundary is created from the segmented volume. Instep f), a watershed surface is created by applying a watershed processto the inverse distance map to identify potential locations forintroducing cracks. In step g), a revised segmented volume based upon agiven degree of revision is produced; which comprises: 1) selecting awatershed grey-scale cut-off value, 2) finding all voxels in thegrey-scale digital volume which have their grey-scale value between thegrey-scale value of the pores and the watershed cut-off value, 3)finding among those voxels the voxels co-located with potentiallocations for introducing cracks identified by the watershed process,and 4) converting the corresponding voxels of the segmented volume tovoxels representing pore space. In step h), trial values are derived forthe select elastic property and porosity from an analysis of the revisedsegmented volume. In step i), the trial values for the select elasticproperty and porosity with the criterion curve are compared, and thegrey-scale watershed cut-off for reallocating pore space is adjusted,and steps e)-i) are iteratively repeated until trial values satisfy thecriterion curve and before proceeding to step j). In step j), animproved segmented volume which incorporates the cracks of the adjustedsegmented volume is produced and stored. In step k), the improvedsegmented volume is used to derive the final absolute permeabilityvalue.

The present invention also relates to a method for increasing theaccuracy with which a segmented volume represents a material samplehaving sub-resolution structure, which comprises steps a)-e). In stepa), a grey-scale 3-D digital image of the sample is obtained. In stepb), a preliminary segmented volume corresponding to the sample isobtained by processing the grey-scale image through a segmentationprocess. In step c), a criterion relation which is developedindependently of the segmented volume is defined as a function of a pairof criterion properties related to a target property. In step d), anadjusted segmented volume is created through additional processing,which comprises 1) applying a processing step identifying locations forpotentially revising structural features of the segmented volume, and 2)determining the degree to which revisions to structural features are tobe realized in revising the segmented volume by identifying the adjustedsegmented volume associated with values for the pair of criterionproperties that satisfies the criterion relation. In step e), therevised structural features of the identified adjusted segmented volumeare stored for use in further digital rock physics applications.

Computerized systems, computer readable media, and programs forperforming the methods are also provided.

The present invention also relates to a segmented digital volume whichrepresents a sample of a porous media, which comprises a) voxelsrepresenting pore space derived from segmentation of a 3D grey scaledigital image, b) voxels representing at least one solid material phasederived from segmentation of the 3D grey scale digital image, and c)converted voxels representing structural features not fully resolved inthe 3D grey scale digital image or the direct segmentation thereof. Theplacement of the converted voxels is derived from additional processingsteps using data from the 3D grey-scale digital image and one or moresegmented volumes derived therefrom, and the volume of converted voxelsin place is solved to satisfy a criteria relation representative of thesample and independent of the 3D grey-scale image.

It is to be understood that both the foregoing general description andfollowing detailed description are exemplary and explanatory only andare intended to provide a further explanation of the present invention,as claimed.

The accompanying drawings, which are incorporated in and constitute apart of the application, illustrate features of the present inventionand, together with the description, serve to explain the principles ofthe present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a core from which a rock samplefor investigation can be selected according to an example of the presentapplication;

FIG. 2 is an isomeric view of a 3D grey-scale digital image of theselected rock sample according to an example of the present application;

FIG. 3 is a work flow diagram according to an example of the presentapplication;

FIG. 4 is a work flow diagram of applying a watershed process inrevising the segmented volume according to an example of the presentapplication;

FIGS. 5-10 are a set of segmented volumes illustrating degrees ofrevision to levels of introduced pore space interconnectivity accordingto an example of the present application;

FIG. 11 is a graph illustrating an elastic criterion curve and acalibration curve defined by derived values for criterion propertiesassociated with revisions of the segmented volume according to anexample of the present application;

FIG. 12 is a graph illustrating a measure of the target property as afunction of the degree of revision according to an example of thepresent application; and

FIG. 13 shows a system according to an example of the present invention.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

The present invention relates in part to a method for increasing theaccuracy of a target property value derived from a sample of a porousmedia using digital imaging techniques. The method can be particularlywell suited to investigating rock samples with techniques of digitalrock physics and is hereafter illustrated in the context of suchapplications, but not limited thereto. For example, the target propertyvalue improved by methods of the present invention can relate to astructure that affects a fluid transport property of the sample, such ascracks providing connectivity between pores space. These cracks or otherstructures that can affect rock properties of interest may be difficultto accurately identify and resolve using conventional digital rockphysics techniques. For example, this improved accuracy can be providedwith methods of the present invention as applied to digital imagingscans of rock samples or other porous media under circumstances in whichresolution available in an initial digital image may be insufficient toeffectively directly capture data that accurately represents total porespace connectivity. The present invention also relates in part toproviding a segmented digital volume which can more accurately representthe actual three-dimensional structure of a sample of a porous media.

The present invention also relates in part to a method for increasingthe accuracy of a target property value derived from a rock samplewherein the sample is scanned to obtain a tomographic digital image,such as a grey-scale image, that can be processed to pore space andsolid material phases through a segmentation process. A process isemployed for revising the segmented volume, e.g., by increasing porespace connectivity, in a manner affecting the value for the targetproperty that would be derived. The degree of revision can beconveniently expressed as function of criterion property values, suchas, for example, a pair of properties which is referred to herein as a“criterion pair,” and an appropriate degree of revision or adjustment tobe solved can be that degree for which the derived values for thecriterion properties satisfy an independently derived criterionrelationship. Applying that degree of revision produces the adjustedsegmented volume, which is used as an improved representation of thestructure of the rock sample under investigation and can be used toderive an improved value for the target property. Another methoddisclosed increases the accuracy with which a segmented volumerepresents a material sample having structure which is not adequatelyresolved in an original three-dimensional tomographic digital image,such as an original grey-scale 3D digital image.

The present invention also relates to a method for revising or adjustingthe representation of a segmented volume corresponding to the sampleunder investigation to account for sub-resolution and/or under-resolvedfeatures. This adjustment can derive from context grounding theresulting segmented volume to spatial placement to re-allocate voxelswithin the volume as a function of data obtained from the sample. Thenet effect or degree of adjustment can also calibrated or indexed basedon objective criteria obtained independent of the tomographic digitalimage (e.g., grey-scale image) and the attendant limitations fromscanning technologies and/or computing technologies.

In methods of the present invention, a three-dimensional tomographicdigital image (e.g., a grey-scale digital image) of a rock sample can beobtained, for example, from scanning operations and an initial segmentedvolume can be produced by processing the grey-scale volume to pore spaceand one or more solid material phases through a segmentation process. Aprocess for adjusting or revising the digital volume can be employed forintroducing feature revisions to the segmented volume which derivespatial placement in the resulting adjusted segmented volume as afunction of both the original grey-scale volume and the directly derivedpreliminary segmented volume. Suitable adjusting techniques which can beused can include, for example, both the watershed application to theinverse of the distance function and gap-filling techniques such asshown herein, as well as other transforms and techniques such asdilation or erosion applications.

The indicated revision of the segmented volume can be performed toaddress sub-resolution and/or under-resolved features in a manneraffecting the value for the target property that would be derived. Asindicated, the degree of revision can be conveniently expressed asfunction of a pair of properties, e.g., as a “criterion pair.” Thecriterion pair can be selected for their relation to the targetproperty, degree of revision, ease of deriving values from a segmentedvolume, and known interrelation independent of the segmented volume. Acriterion relation (which for convenience, can be referred to as “acriterion curve”) can be expressed as a function of the pair ofcriterion properties, wherein the criterion relation is obtained fromsources independent of the preliminary and revised segmented volumes andis compared with values for the criterion pair derived from the revisedsegmented volume. Instead of a criterion curve, a look-up table,database, and the like, can be used. The appropriate degree of revisionor adjustment can then be solved for as that degree of revision forwhich the volume-derived values for the criterion properties satisfy thecriterion relation or curve. Applying that degree of revision producesthe adjusted segmented volume which can be used as an improvedrepresentation of the structure of the rock sample under investigation.This adjusted segmented volume can be stored on the computer andaccessed to derive values for target properties such as absolutepermeability. Further, those structural features can be combined withother data to produce an improved segmented volume which morerealistically represents the rock sample overall. The resulting improvedsegmented volume can be stored in a computer from which it may bedisplayed or accessed for simulations, modeling, or computationsincluding deriving improved values for additional properties. Forexample, the improved segmented volume can be used to derive the targetproperty value, such as described herein.

Certain nomenclature has been adopted for the sake of consistency inthis application. For example, as used herein, a “preliminary segmentedvolume” is the initially segmented volume unrevised and unadjustedthrough the practice of this invention. As used herein, “revisedsegmented volume” is a segmented volume prepared in the course ofpracticing the invention while the “adjusted segmented volume” is thatrevised segmented volume having revised structural features that satisfythe criterion relation. As used herein, the “improved segmented volume”has the revised structural features of the adjusted segmented volume andmay also be populated with such other data as may be appropriate forapplication in desired simulations and deriving desired property values.

The present invention also relates to a method for increasing theaccuracy with which a segmented volume represents a material samplewhich has structure that is not adequately resolved in an originalgrey-scale 3D image or other original three-dimensional tomographicdigital image. By way of example, this method can be applied to developan adjusted absolute permeability value k from data acquired in anoriginal 3D grey-scale image with insufficient resolution to effectivelyimage pore space connectivity. The grey-scale image can be obtained fromscanning through sequential cross sections of the rock sample,grey-scale characterization values are assigned, and the integratedimage can be segmented to produce an initial or preliminary segmentedvolume composed of voxels representing pore spaces and voxelsrepresenting one or more solid material phase(s). A preliminary valuefor the target property can be obtained from the preliminary segmentedvolume. The preliminary value can be considered in the context of therock sample and the location of its collection. A benefit of the presentinvention can become evident when the preliminary value is not areasonable match to expectations.

In methods of the present invention, a criterion curve can be developedindependently of the segmented volume as a function of a select elasticproperty (conveniently, elastic wave velocity V_(p)) and porosity φ. Aninverse distance map can be created of the pore space to the solidmaterial phase boundary from the initial or preliminary segmentedvolume. For each phase, a characteristic grey-scale value can beselected, which represents the grey-scale value corresponding to thisphase in absence of interference caused by phase boundaries. A watershedprocess can be then applied to the inverse of the distance map. Itproduces a watershed surface in the 3-D space associated with thesegmented volume. This surface can pass through the narrowestconnections between solid grains in the rock sample. This particularapplication takes advantage of the observation that the under-resolvedconduits, such as those between pore spaces, are usually located inthese narrow connections, and can be visually identified in thegrey-scale digital image as lines of voxels having grey-scale valuesbetween the characteristic grey-scale values for pore and solidmaterial, thus representing potential locations in the segmented volumefor introducing “cracks”. A revised segmented volume can be producedbased upon the degree to which these potential cracks are realized. Todo this, a grey-scale watershed cut-off value can be selected forwatershed application, and all voxels in the grey-scale image can beidentified which have their grey-scale value between the characteristicgrey-scale value for the pores and the watershed cut-off value areidentified as candidate voxels. From among these, those voxelsco-located with “potential cracks” delineated by watershed surfaces canbe identified and the corresponding voxels of the segmented volume canbe converted to voxels representing pore space. This, in effect,introduces new features to the volume as cracks providing pore spaceconnectivity.

Trial values or calibration values for elastic property V_(p) andporosity φ can be derived in methods of the present invention, forexample, from an analysis of the revised segmented volume and thesevalues are compared with a criterion relation which may conveniently beexpressed in the plot of a criterion curve. An iterative solution,varying the grey-scale watershed cut-off value and changing the revisedsegmented volume accordingly, can be conveniently employed to identifythe cut-off point at which the associated segmented volume producestrial values satisfying the criterion relation. The revised segmentedvolume associated with this solution is the adjusted segmented volumeand the revised features thereof can be used in an improved segmentedvolume to derive the final value for the target property representativeof the rock under investigation, e.g., a more realistic absolutepermeability value in this example. Methods of the present inventionalso can be used, for example, to increase the accuracy with which asegmented volume represents a material sample having structure notadequately resolved in an original grey-scale 3D image or other originalthree-dimensional tomographic digital image. A segmented digital volumethat can more accurately represent a sample of a porous media also canbe provided by methods of the present invention. This segmented digitalvolume can be electronically displayed, printed on a tangible medium, orboth, or can be produced or represented in other forms.

FIG. 1 is a schematic illustration of a core 10 secured from drillingoperations which allow such rock samples to be cut and retrieved to thesurface intact as a preferred source of rock samples for detailedinvestigation using digital rock physics. Studying such cores providesan enhanced opportunity to understand the specific characteristics ofthe rock at that location. A robust understanding of rock properties atmultiple locations in the field then serves as the best foundation tobetter understand the reservoir and to facilitate interpreting otherdata such as seismic or logging data.

Although illustrated with core analysis of rock samples, it should beunderstood that the present invention can be applied to other materialsbesides natural rock. As to rock, it can be applied to percussion plugs,rotary cores, drilling cuttings, or samples of rock otherwise collected.For scanning, the type of sample preparation can depend upon the imagecapture method to be used. For example, samples can be cleaned, shaped,mounted, or prepared with other techniques typically used for preparinga rock sample for image capture on the type of image scanning instrumentto be used. The preparation of samples, for example, can comprisecutting, abrading, shaping milling, focused ion beam polishing, othertechniques to alter the size and shape of rocks, or any combinationsthereof. For example, the samples have or are provided in sizes andshapes which can ensure that the object fits inside the field of view ofthe scanner and that it does not move during the scan. Cylinder shapesare efficient for scanning, but the sample shapes are not limitedthereto.

Digital rock physics is an important tool for facilitating a moreaccurate and rapid understanding of rock properties of interest and ofvalue to reservoir engineers in applications including, but not limitedto, well planning, completion design, reservoir management and reservoirestimates. In accordance with an illustration of practices of thesetechniques, natural rock samples can be scanned through sequentialtwo-dimensional (2D) cross sections (such as schematically representedby planes 11 a-11 e in FIG. 1), which are used to produce tomographicdigital images, such as digital grey-scale images 12, such asillustrated in FIG. 2, which have 3D visual effects, and which arereferred to herein as 3D images. For example, the images 12 can visuallyconvey 3D information on a volume of the scanned sample which can bedisplayed in or on a two-dimensional medium (e.g., LCD, LED-LCD, plasmadisplay, CRT display, projection screen display, printed paper, etc.).Suitable scanning operations can employ, for example, X-Ray computedtomography scanning (CT scanning), focused ion beam scanning electronmicroscope (FIB-SEM scanning), magnetic resonance imaging, or other 3-Dgrey-scale imaging techniques generally capable of useful resolution anddigitization, including magnetic resonance imaging and otherapplications of microtomography or microradiography technology.Typically, X-ray CT scanning is non-destructive to the scanned portionsof the sample, whereas FIB-SEM is destructive to scanned portions of thesample. A rock sample can be scanned, for example, with an X-ray CTscanner, which can have a resolution down to <1 micron, or higherresolution X-ray CT scanners can be used, which can have a resolutiondown to 50 nanometers (nm), or other values. A FIB-SEM workstation canbe used which has a resolution, for example, of from about 5 nanometersto about 30 nanometers, or other values. X-ray CT scanners and FIB-SEMworkstations are commercially available which can provide theseresolutions. Software typically supplied with or provided for commercialscanning machines, which can generate 2D grey-scale images for thedifferent scanned sections of the sample. A 3D grey-scale image of athickness portion of the sample can be obtained as a stack of the 2Dgrey-scale images acquired by scanning through a thickness of thesample. Further processing of 3D grey-scale images 12 such as shown inFIG. 2 through segmentation steps can produce a segmented volume 14A ofelemental voxels that are characterized as either pore space 16 or solidmaterial phase(s) 18, such as illustrated in FIG. 5.

Circumstances are sometimes encountered, however, in which the value ofa given target property derived from such segmented volumes can beunreliable when the segmented volume is produced directly from thescanned data alone. For instance, very thin conduits connecting thepores in samples from some reservoir rock represented by core 10 may bedifficult or impossible to image with digital rock physics usingconventional arrangements. For example, very thin connecting conduitsbetween pores in samples may be smaller than or otherwise outside theeffective resolution and/or computational thresholds or limitations ofthe scanning equipment that is used. It can be problematic or impossibleto directly and accurately resolve this structure for production of 3Dimages thereof, such as due to an insufficient highest availablemagnification on the scanning equipment that is used or as a result ofcomputational challenges for a given magnification in combination with arequired field of view. The present investigators have recognized thatthis can be a common situation for some shales, for example, tightcarbonates or sandstones, and some igneous rock samples. In such cases,the grey-scale image 12 (FIG. 2) cannot achieve the resolution necessaryfor pore space connectivity to be accurately deduced through theapplication of the usual segmentation techniques. The segmented volume14A of FIG. 5 represents a segmented volume produced from scanned dataalone and without use of a method of the present invention. In suchcases of producing segmented volumes from scanned data alone such asshown in FIG. 5, the usual analytic techniques deriving values from anunadjusted segmented volume 14A can yield unreliable results forproperties such as absolute permeability, relative permeability,capillary pressure, electrical resistivity, elastic properties, andother rock properties. For instance, a Lattice-Bolzmann solution toNavier-Stockes equations (i.e., the Lattice-Bolzmann Method or “LBM”) asdiscussed, e.g., in Toelke (2010), may yield an estimated absolutepermeability for rock that is unrealistically small or even at zero Thiserror can become known where production data may indicate asubstantially greater permeability is actually present than estimatedwith LBM. A need that can be met by a method of the present invention isindicated in such instances where the preliminary values estimated forthe target property do not match the expected values.

FIG. 3 is a work flow diagram 22 illustrating a practice of the presentinvention for more realistically characterizing rock structure in asegmented volume of pore space and solid material phase(s) from whichimproved values of a target property can be obtained despite challengesto directly scanning structure in the rock sample that influence thetarget property values, e.g., the challenges associated with the imagingof cracks providing pores space connectivity and affecting fluidtransport properties.

In step 30, a three-dimensional tomographic digital image, such as a 3Dgrey-scale image 12 (FIG. 2), is obtained from an integrated scan 30 ofthe rock sample 10 of FIG. 1. A sequence of cross sectional images isschematically illustrated as x-y planes 11 a-11 e. Many images can besequentially obtained in these methods and then combined by stacking andaligning them in the proper position, to create a preliminarythree-dimensional (3D) volume. The scan image output produced by a CTscanner, for example, can be a 3D numerical object including a pluralityof 2D slices or sections of the imaged sample. Each 2D image can includea grid of values each corresponding to a small region of space definedwithin the plane of the grid. Each such small region of space can bereferred to as a “pixel” and can be assigned thereto a numberrepresenting the image darkness (or for example the density of thematerial) determined by the CT scan procedure. The process by which thetwo-dimensional images are stacked and aligned is not specificallylimited. The grey scale images can be stacked and aligned, for example,with commercial software application for scientific and industrial datavisualization and analysis available adapted for use in the presentmethods. Stacking can be done, for example, by sequentially positioningthe images of the slices in the order they were obtained from thesample. Alignment can rely on processing techniques which identify thecorrect lateral position of one slice relative to the next in the samestack.

The grey-scale image is initially segmented in step 32 in FIG. 3 and canbe characterized as either pore space 16 or one or more solid materialphases 18 content (see FIG. 5). The form of segmentation depends uponthe type of rock and type of properties under investigation. Forinstance, for a target property of absolute permeability alone, it canbe sufficient to segment to only two phases, one for pore space and onephase for solid material. Other properties and more complex mineralogycan be characterized with multiple solid material phases whereapplicable. Further, these options can be combined. As further shownherein, a multiple phase segmentation can be simplified to facilitaterevising the segmented volume or for improving the value obtained forabsolute permeability alone by replacing all solid material phases withthe same value. This provides the same simplicity for this part of theanalysis as binary segmentation, yet can preserve identification ofmultiple solid material phases that may be reintroduced with reassigneddistinct phase values for an improved segmented volume after thestructural features responsible for pore space connectivity have beenadjusted. Alternatively, if features are adjusted in a binarysegmentation, data may be exported to or imported from a separatecompatible segmentation from the same scanned volume to populate animproved segmented volume.

For either alternative, the simplicity of working with only twocharacterizing values has been found to produce a good and acceptablerange of usefully guided and controlled revisions. Alternatively, insituations where any limitations of computer memory, computationalresources, and computation time are not at risk of being reached,revisions can be undertaken directly to produce more sophisticatedsegmented volumes having a greater number of uniquely characterizedphases during the revision process.

For purposes herein, “segmentation” means a process of partitioning adigital image into multiple segments (sets of pixels). Imagesegmentation is typically used to locate objects and boundaries (lines,curves, etc.) in images. In segmentation of porous rock, for example, itcan be used to allocate pore space and one or more non-porous phaseregions and their boundaries. Image segmentation is the process ofassigning a label to the pixels in an image such that pixels with thesame label share certain visual characteristics. The result of imagesegmentation is a set of segments that collectively cover the entireimage, or a set of contours extracted from the image. Each of the pixelsin a region can be similar with respect to some characteristic orcomputed property, such as color, intensity, or texture. Adjacentregions are different with respect to the characteristic(s).General-purpose algorithms and techniques have been developed and usedfor image segmentation in the field of digital image processing. Forexample, a digital image of a rock sample can be segmented into itscompositional classes. The term “compositional classes” can encompass,for example, open pores, mineral(s), optionally other types ofmaterials, or any combinations thereof. Members of a singlecompositional class should possess the same composition and the samegeneral structure relative to other compositional classes so that theyinfluence to a similar extent the properties of the rock. As known inthe field, there can be ambiguity in segmenting x-ray attenuation images(to use the X-ray microtomography example) into compositional classes ofsimilar mineralogy because different rock minerals can have similarx-ray attenuations. Segmentation can be greatly aided if priorinformation about the mineral composition of the sample limits thenumber of possibilities for each pixel. As also known, where there is noprior information, x-ray diffraction (XRD) can be used to determinemineralogy. If two compositional classes have equal or nearly equalx-ray attenuations, it may be necessary to use structural metrics todistinguish them as will be understood by those skilled in the art.These and other segmentation methods and techniques may be applied oradapted for use in a method and system of the present invention.

The segmented volume 14A that is produced with step 32 of FIG. 3 isillustrated in FIG. 5 for which the lack of pore space connectivity canbe seen, e.g., by comparison to segmented volume 14F of FIG. 10 forwhich pore space connectivity is more clearly apparent in the form ofnumerous cracks or conduits 24. A problem arises when there is asignificant and effective connectivity between the pores in the actualrock sample, but it largely resides in cracks or other conduits toosmall to be resolved in the grey-scale image in a meaningful manner thatcan be characterized through segmentation processes, such as theindicated segmentation process. In this situation, a correspondingpreliminary value for a target property derived from segmented volume14A of FIG. 5 will prove to be unreliable to the extent that property isin any way related to effective pore space connectivity. A considerationof the preliminary value demonstrating this failure to matchexpectations should then lead to application of the present invention.

The present invention relates in part to a method for increasing theaccuracy of a target property value by deriving the value from anadjusted segmented volume, which is illustrated herein, for example, asvolume 14E in FIG. 9. In FIG. 3, a calibrating step 34 is used toproduce the adjusted segmented volume using inputs from both theoriginal grey-scale image 12 (FIG. 2) obtained from scan 30 and thedirectly processed segmented volume 14A (FIG. 5) segmented at step 32.These inputs provide guidance on spatial placement for where cracks orconduits 20 may be introduced to segmented volume 14B (FIG. 6) guided byresolvable structure. This guidance is generally set forth ascontribution 34A to calibrating step 34, but this contribution drivestoward a range of possible revisions as a function of the degree ofrevision, i.e., the volume of cracks that are actually introduced into arevised segmented volume produced in step 42. Here various degrees arerepresented by revised segmented volumes 14B-14F in FIGS. 6-10,respectively. Since each of revised segmented volumes 14B-14F willproduce different target property values, it is important to identifywhich of these possibilities to use to derive the final target propertyvalue. For instance, consider the graph of FIG. 12 in which absolutepermeability values K_(A), K_(B), K_(C), K_(D), K_(E), and K_(F) havebeen derived and plotted for each of segmented volumes 14A-14F in FIGS.5-10, respectively. In FIG. 12, the indicated absolute permeabilityvalues are plotted as Log 10 permeability (nD) values as a function ofporosity (φ). Absolute permeability value K_(E) is a value at 80%watershed.

Developing an appropriate criterion relation, illustrated here as thestep of obtaining an independent criterion curve 36 in FIG. 3, providesan objective means to identify an appropriate degree of revision, i.e.,to identify the appropriate revised segmented volume, here adjustedsegmented volume 14E of FIG. 9, to use for further analysis. Identifyingthe appropriate degree of revision is generally referenced ascontribution 34B of calibration step 34 in FIG. 3. Together,contribution 34A of adding the location of possible cracks or conduitswith the spatial positioning guided by the original segmented volumecombined with contribution 34B determining the degree that such featuresare realized, produces a robust calibration process 34 in support ofderiving a more accurate value for the target property in step 48.

FIG. 11 illustrates criterion curve 38 in graph 40. This criterion curveis expressed as a relation of two criterion properties, porosity φ andelastic property V_(p) (km/sec), in this example. The criterionproperties are selected for a relationship with the target property,sensitivity to the degree of revision, and for an interrelationship toeach other that can be expressed independent of the segmented volume,e.g., it can be calculated based upon a theoretical rock physics model,calculated with an empirical transform, derived from a number ofhistorical data point relevant to the rock sample, etc.

Solving for the degree of revision in the segmented volume thatsatisfies the independent criterion curve identifies the adjustedsegmented volume 14E for use in deriving a more accurate target valueand to provide revised structure to an improved segmented volume, withreference made to step 48 in FIG. 3.

In accordance with one practice of the example in FIG. 3, thecalibrating step 34 can conveniently be an iterative process wherein thegrey-scale image 12 (FIG. 2) obtained in step 30 and the segmentedvolume 14A produced therefrom (see FIG. 5) are used to revise thesegmented volume at step 42 from which calibration values are derivedfor criterion properties in step 44. Calibration values derived for thecriterion pair from the revised segmented volume are compared with theindependent criterion curve in step 46. If the derived values satisfythe criterion curve 38, that volume is the adjusted segmented volumehaving the revised structural features to be used. If not, iteration 49shown in FIG. 3 is proceeded with and repeated until the appropriateadjusted segmented volume is identified.

Degrees of revision resulting in segmented volumes 14A-14F (FIGS. 5-10)produce criterion pair values C_(A), C_(B), C_(C), C_(D), C_(E), andC_(F), defining calibration curve 52 in FIG. 11. Criterion Pair valueC_(E) is a value at 80% watershed. As shown in FIG. 11, calibrationcurve 52 crosses criterion curve 38 at point C_(E) which is associatedwith segmented volume 14E of FIG. 9. Adjusted segmented volume 14E withamended structural features provides a more realistic representation forpore space connectivity and can be used directly in step 48 to providean improved absolute permeability value as a target value property.Alternatively, structural features in adjusted segmented volume 14E canprovide an opportunity to derive a number of more realistic propertyvalues as a contribution to an improved segmented volume in step 47combining with other data. For instance, these structural features canbe retained or inserted in order to populate an improved segmentedvolume having the benefits of this structure, but without theassumptions and simplifications that had a transient purpose infacilitating the development of a better representation ofsub-resolution and under-resolution structure in the rock. Thus, if asingle solid material phase was assumed for this process, it can bereplaced with additional data from a corresponding and compatiblesegmented volume with multiple solid material phases which betterrepresent local mineralogy. Or, if multiple solid material phases werecharacterized with a single value for the purposes of revisingstructural features in the adjusted segmented volume, values can beinserted to apply distinct values among each of the individual solidmaterial phases. For example, the additional data can constitutediscrete grey-scale values which characterize a plurality of the solidmaterial phases. This improved segmented volume is an overall betterrepresentation of the rock sample that can have a broader applicationthan absolute permeability alone as the target property or even a groupof fluid flow properties.

This improved value is herein sometimes referred to as a “final value”for the target property or properties. However, it is to be understoodthat the combination with other insights or analysis in the practice ofthis method may be possible and does not detract from the benefitsafforded by the practice of this invention, as claimed, should a laterstep in any way further alter this “final value.”

A particularly useful application of the present invention is addressedin the work flow diagram of FIG. 4. Scanning the rock sample 60 producesa three-dimensional tomographic digital image, such as the 3D grey-scaleimage (volume) 12 illustrated in FIG. 2. Returning to FIG. 4, segmentingthe volume 62 converts the grey-scale image to produce segmented volume14A of FIG. 5 having voxels initially characterized as pore space 16 andsolid material phase(s) 18. Creating a distance map 64 then measures thedistance from each voxel of the pore space 16 to boundaries withmaterial 18, with reference made to FIGS. 4 and 5, respectively.

Applying a watershed process 66 to an inverse of the distance mapproduces a watershed surface that identifies potential locations forintroducing cracks or conduits into the revised segmented volumes.Watershed techniques are generally discussed, e.g., in Vincent (1991)and other publications. The watershed algorithm (or transform) is awell-established image-processing technique for grey-scale images. It isbased on a topographical interpretation of the gradient image. Thedensity magnitude is considered as a topographical relief where thebrightness value of each voxel corresponds to physical elevation. The“water flowing down” the elevation always follows the gradient direction(the direction with the maximal density change) to the nearest localminimum. Areas with common local minimum constitute watershed regions,and the borders between these regions constitute watersheds. Theprocedure results in partitioning of the image in catchment basins, theborders of which define the watersheds. The watershed algorithm can beused to create closed borderlines, which can be used for segmentation.Vincent (1991) shows an application of the watershed algorithm whichdivides the gradient field into a set of spatially connected regions,each of which is “smooth” in its interior. Thus, these regions arecharacterized by having strong gradients at their boundaries. Since thegradient value is proportional to the (perceptual) difference intexture, by calculating the distance metric as above, the image issegmented into regions of homogenous texture. In addition to Vincent(1991), illustrations of the watershed algorithm are provided, forexample, in U.S. Pat. Nos. 6,728,314, 6,947,591, 6,956,961, 7,327,880,and 7,333,646, which are incorporated herein in their entireties byreference.

Any other processes for introducing pore space connectivity based ondifferent algorithms may alternatively be employed, e.g.,dilation-erosion. Further, pore space connectivity can be modeled with aplurality of small tubes as conduits instead of area cracks as inwatershed.

In the illustrated example shown in FIG. 4, watershed application 70combines guidance for preferred spatial placement for introducing porespace connectivity from the watershed surface of step 66, data fromscanning the rock 60, and an input in the form of selecting an initialwatershed cut-off value 72. All voxels having a grey-scale value betweenthis cut-off and the grey-scale value characteristic of the pore spaceare identified. Of these, those voxels that are also co-located withpotential locations for introducing cracks identified by the watershedsurface are converted into pore space 16. Realizing these cracks orconduits 20 changes the values for many properties that can be derivedfrom the revised segmented volume, including, but not limited to, thoseof porosity, elastic properties, absolute permeability, relativepermeability, capillary pressure, the electrical formation factor, andother rock properties.

Common practice is to take the mode, i.e., the peak of the porespace-grey scale values histogram, of the voxels from grey-scale image12 of FIG. 2 that corresponds to the pore space characterized in initialsegmented volume 14A of FIG. 5. Other methods can be used to determinethe grey-scale value characteristic of the pore space, e.g., mean valueof all pore space grey-scale values, an average grey-scale value in thecenter of the largest pore, etc. As illustrated in FIG. 4, this has beengenerally designated as step 65 of determining a grey-scale valuecharacterization of the pore space with input from the originalgrey-scale image from scanning the rock 60 and the original segmentedvolume from segmentation step 62. The output of step 65 is an input tostep 70 for applying the watershed. Step 78 in FIG. 4 comprisesdeveloping an independent criterion curve 38 relating a select elasticproperty with porosity, such as discussed herein with respect to FIG.11. This criterion curve can be developed, for example, from atheoretical rock physics model, recognized empirical velocity-porositytransform, or simply a number of data points relevant to the rock underexamination. For example, the development of the criterion curve cancomprise deriving a relationship from a number of data points relevantto the material sample, wherein the data are obtained from laboratorymeasurements, or data from others sources such as field-based well data,such as well logging data (e.g., wireline logging data,logging-while-drilling (LWD) data, or measurement-while-drilling (MWD)),or from more than one of these sources of data.

Dvorkin et al (2011) discusses the use of laboratory data and analysisof the “stiff sand model” (E152). The stiff sand model is furtherdiscussed in Mavko, G., et al (2009), The rock physics handbook: Toolsfor seismic analysis of porous media, Cambridge: University Press,(hereinafter, the “Mavko (2009)” publication), in constructingelasticity and porosity pairs (pp. 260-262). By way of another example,Mavko et al. (2009) discusses the Raymer transform (also known as theRaymer-Hunt-Gardner functional form) (p. 379). This is a mathematicalformula derived from a statistical fit of extensive laboratory data andrelating porosity φ and elasticity through compressional wave (P-wave)velocity V_(p) expressed as follows:V _(p)=(1−φ)² V _(ps) +φV _(pf)where: V_(ps) is the P-wave velocity in the solid material phase; andV_(pf) is the P-wave velocity in the pore fluid.

It is suitable for these purposes to simplify this on the assumptionthat all that is not pore space in the rock sample is solid materialformed from a single, pure, solid material, e.g., a pure rock or puremineral, such as pure quartz, for V_(ps). Similarly, V_(pf) may beassumed to have no significant contribution for the present purpose ofcharacterizing the structure of the rock sample. With thesesimplifications, it is straightforward to develop a range of values forporosity φ in relation to elasticity represented by V_(p). Howeverdeveloped, this relation can be conveniently presented as elasticcriterion curve 38 in graph 40 of FIG. 11. Select elastic properties canprovide particularly suitable criteria in this application because someare very sensitive to changes due to the presence of thin pores that mayextend over a 2D area as “cracks” and compressional wave velocity V_(p)is a particularly convenient track for elasticity. The compressionalmodulus of elasticity M would be similarly suitable for thisillustrative application. Values of selected elastic property may bederived by replacing all mineral phases in an adjusted segmented volumesuch as described herein by one selected mineral, for which thecriterion relation can be obtained. The selected mineral can be one ofquartz, calcite, dolomite, or any other mineral.

Other pairs of properties may serve as the criterion pair. What islooked for is that the relationship between the criteria pair bedefinable both with, and independent of, the segmented volume and thatthe criteria pair be sensitive to the method of revision and bear arelationship with the target property. For instance, if additionalprocessing steps were introducing single voxel “lines” of tubes orconduits rather than the 2D area “cracks” of watershed, porosity φ andthe electrical resistivity formation factor FF present a more effectivecriterion pair. These can be solved for the criterion relationshipthrough experimental data or for example, the Humble formula, such asdiscussed in Tiab, D., et al. (2012), Petrophysics: Theory and practiceof measuring reservoir rock and fluid transport properties, GulfProfessional Publishing, 239-245), as a modification of Archie'sequation.

Referring again to FIG. 4, applying the watershed 70 with cut-offproduces a revised segmented volume 14F of FIG. 10, which is used tocalculate calibration values 74 for a select elastic property and forporosity.

The porosity φ represented in revised segmented volume 14F can be simplycalculated as the number of voxels characterized as pore space dividedby the total number of voxels in the segmented volume.

The elastic moduli, including compressional modulus M, can be derivedfrom the revised segmented volume using finite element analysis in astatic deformation simulation. The simulation applies stresses to thefaces of the revised segmented volume and the resulting strain isassumed to be a linearly elastic. Further, this is solved for dry rockassuming all that is not pore space is the same pure, solid material asassumed in developing the criterion curve, e.g., pure quartz in thisexample. The effective deformation from stresses applied at theboundaries is then used to calculate the compressional modulus M, fromwhich the P-wave velocity V_(p) is solved as:V _(p) =√M/ρwhere: M is the compressional modulus and ρ is the bulk density.

The bulk density is readily available knowing the porosity and applyingthe assumption of a single material for all voxels in the solid materialphase.

These volume derived values for porosity φ and a select elastic property(e.g., P-wave velocity, V_(p)) are the calibration values and arecompared with the criterion curve in step 76 shown in FIG. 4. Forexample, graph 40 of FIG. 11 plots calibration curve 52 againstcriterion curve 38 as a function of porosity and elastic wave velocity.

In this example, an iterative form of solution is employed and it isconvenient to overshoot the degree of adjustment in selecting theinitial cut-off in step 72 shown in FIG. 4. This results in a revisedsegmented volume 14F as illustrated in FIG. 10 with introducing of morecracks and more pore space interconnectivity than expected in the rock.FIG. 11 illustrates bounding the solution with a low watershed cut-offpoint and incrementally advancing through increasing watershed cut-offpoints represented with the iterative loop at step 82 shown in FIG. 4.For example, an initial grey-scale watershed cut-off can be selected forreallocating pore space in the revised segmented volume which is higherthan present in the rock sample. Then, the grey-scale watershed cut-offcan be incrementally adjusted for reallocating pore space wherein theadjusting can proceed incrementally from low to high values of thegrey-scale watershed cut-off values. In FIG. 11, arrow 51 illustratesthe trend line of changes to the criterion pair and greater degrees ofrevision. These iterations produce revised segmented volumes 14B, 14C,14D and 14E (FIGS. 6-9) associated with derived criterion pairs C_(B),C_(c), C_(D) and C_(E), respectively, each plotted in FIG. 11 anddefining calibration curve 52 illustrating this relationship.

Once the calibration values derived from the revised segmented volumesatisfy the criterion curve, as at point C_(E) on FIG. 11, that revisedsegmented volume, here volume 14E of FIG. 9, becomes the adjustedsegmented volume and is used to derive the absolute permeability valuefor the target property in step 80 shown in FIG. 4.

If the target value is absolute permeability, an improved and moreaccurate value can be obtained, for example, from the adjusted segmentedvolume using the LBM to solve Navier-Stokes equations as discussed aboveto derive the final value.

Since this adjustment addresses pore space connectivity, the values forother target properties for which pore space connectivity is important,e.g., other fluid flow properties, may be similarly improved. Forinstance, other properties for which target values may be improvedthrough this technique, include, but are not limited to, relativepermeability k_(rel) capillary pressure P_(c), and electricalresistivity formation factor FF, see, e.g., Dvorkin (2011). And, in thecourse of using a criterion pair of elastic property V_(p) and porosityΦ, more realistic values were already identified with the adjustedsegmented image. However, as discussed above, it can be advantageous tofirst populate the adjusted segmented volume with additional data in animproved segmented volume as groundwork (see optional step 84 in FIG. 4)for application in deriving additional values beyond absolutepermeability (see step 86 in FIG. 4).

Further, the depositional formation of the rock samples are known toproduce some properties having an anisotropic nature and it can bedesirable to derive improved values for such target properties for eachdirection in the adjusted or improved segmented volumes.

Referring to FIG. 13, a system (100) is shown which can be adapted forperforming the present methods. As shown in this example, threedimensional (3D) images of the porous medium samples obtained fromsource (101) are generated by the scanner (102). The scanner cancomprise, for example, a computer tomographic (CT) scanner, a scanningelectron microscope (SEM), a focused ion beam scanning electronmicroscope (FIB-SEM), or similar device capable of producing a threedimensional digital image of a porous medium. The 3D image output (103)of the scanner can be transferred to a computer (104) having programinstructions for carrying out the 3D image analysis, and the indicatedcriterion and watershed simulation analyses, to generate sample modelingoutput/results which can transmitted to one or more devices (105), suchas a display, a printer, data storage medium, or combinations of these.The computer programs used for 3D image analysis and the CFDcomputations and simulation modeling can be stored, as a programproduct, on at least one computer usable storage medium (104B) (e.g. ahard disk, a flash memory device, a compact disc, a magnetic tape/disk,or other media) associated with at least one processor (104A) (e.g., aCPU or GPU) which is adapted to run the programs, or may be stored on anexternal computer usable storage medium (not shown) which is accessibleto the computer processor. Computer (104) can include at least onenon-transitory readable memory unit (104C) for storage of the programs,input data and output data, and other program results, or combinationsof these. For output display, device (105) can be, for example, adisplay monitor, CRT, or other visual means of display (not shown). Thecomputer (104) may include one or more system computers, which may beimplemented as a single personal computer or as a network of computers.However, those skilled in the art will appreciate that implementationsof various techniques described herein may be practiced in a variety ofcomputer system configurations, including hypertext transfer protocol(HTTP) servers, hand-held devices, multiprocessor systems,microprocessor-based or programmable consumer electronics, network PCs,minicomputers, mainframe computers, and the like. The units of system(100) including scanner (102), computer (104), and output display and/orexternal data storage (105), can be connected to each other forcommunications (e.g., data transfer, etc.), via any of hardwire, radiofrequency communications, telecommunications, internet connection, orother communication means. It is to be understood that the methodsdescribed herein may be implemented in various forms of hardware,software, firmware, special purpose processors, or any combinationthereof.

The present invention includes the followingaspects/embodiments/features in any order and/or in any combination:

-   1. A method for increasing the accuracy of a target property value    derived from a digital image representing a material sample,    comprising:

a) obtaining a three-dimensional tomographic digital image of thematerial sample;

b) generating a preliminary segmented volume corresponding to thematerial sample by processing the three-dimensional tomographic digitalimage through a segmentation process;

c) obtaining a criterion relation developed independently of thepreliminary segmented volume as a function of values of criterionproperties related to the target property;

d) creating an adjusted segmented volume through additional revisingfeatures to the preliminary segmented volume, comprising:

-   -   1) applying a processing step to identify locations for        potentially revising features of the preliminary segmented        volume;    -   2) applying revision features to the preliminary segmented        volume to create a revised segmented volume;    -   3) deriving trial values of criteria properties from the revised        segmented volume;    -   4) repeating at least steps 2)-3) on the revised segmented        volume until trial values of criterion properties satisfy the        criterion relation; and

e) deriving a final value for the target property from the adjustedsegmented volume.

-   2. The method of any preceding or following    embodiment/feature/aspect, wherein the values of criterion    properties are values of a pair of criterion properties.-   3. The method of any preceding or following    embodiment/feature/aspect, wherein obtaining a three-dimensional    tomographic digital image of the material sample comprises scanning    the material sample with at least one of a group comprising: focused    ion beam scanning electron microscope, X-ray computed tomography,    and magnetic resonance imaging.-   4. The method of any preceding or following    embodiment/feature/aspect, wherein the obtaining of the preliminary    segmented volume corresponding to the material sample comprises    processing the three-dimensional tomographic digital image to a    plurality of phases for producing the preliminary segmented volume    as comprised of voxels characterized as either pore space or solid    material phase.-   5. The method of any preceding or following    embodiment/feature/aspect, wherein:

a) the revising of features comprises adding cracks;

b) the applying of a processing step to identify locations forpotentially revising features of the preliminary segmented volumefurther comprises:

-   -   1) creating an inverse distance map of the pore space to the        solid material phase boundaries in the preliminary segmented        volume; and    -   2) applying a watershed processing step for identifying        positions for potentially introducing cracks into the solid        material phase as a function of the inverse distance map; and

c) the obtaining of a criterion relation developed independently of thepreliminary segmented volume as a function of a pair of criterionproperties related to the target property further comprises defining thecriterion relationship using one or more of a group comprising:calculating a theoretical criterion relationship based on a theoreticalmaterial physics model, employing an empirical transform, and deriving arelationship from a number of data points relevant to the materialsample;

d) the creating of an adjusted segmented volume through additionalrevising features to the preliminary segmented volume by revising theadjusted segmented volume until the associated values for the pair ofcriterion properties satisfies the criterion relation, and furthercomprises:

-   -   (1) obtaining a characteristic grey-scale value of the pore        space    -   (2) applying an iterative watershed cut-off value; comprising:        -   i) selecting a watershed grey-scale cut-off value;        -   ii) finding all candidate voxels in the three-dimensional            tomographic digital image which have their grey-scale value            between the characteristic grey-scale value of the pore            space and the iterative watershed cut-off value;        -   iii) finding among those candidate voxels the voxels to be            realized which are co-located with potential locations for            introducing cracks identified in the watershed surface; and        -   iv) converting the voxels identified to be realized in the            segmented volume to voxels representing pore space;        -   v) deriving trial values for criterion properties from an            analysis of the revised segmented volume; and        -   vi) comparing the trial values for the criterion properties            with the criterion relationship, adjusting the grey-scale            watershed cut-off for reallocating pore space and            iteratively repeating steps ii) to vi) until the trial            values satisfy the criterion relationship.

-   6. The method of any preceding or following    embodiment/feature/aspect, wherein:

a) the material sample comprises a rock sample;

b) the pair of criterion properties comprise porosity and a selectelastic property; and

c) the target property is selected from a group comprising: absolutepermeability, relative permeability, capillary pressure, and electricalresistivity.

-   7. The method of any preceding or following    embodiment/feature/aspect, further comprising populating the    adjusted segmented volume with additional properties, and using a    resulting segmented volume to derive additional properties of    interest from the adjusted segmented volume.-   8. The method of any preceding or following    embodiment/feature/aspect, wherein step 4) comprises repeating steps    1)-3) on the revised segmented volume until trial values of    criterion properties satisfy the criterion relation.-   9. The method of any preceding or following    embodiment/feature/aspect, further comprising storing the adjusted    segmented volume created in step d).-   10. A method for increasing the accuracy of a target property value    derived from a digital image representing a porous material sample,    comprising:

a) obtaining a three-dimensional tomographic digital image comprising agrey-scale volume of the sample;

b) obtaining a segmented volume representing the sample by processingthe grey-scale volume to pore space and a plurality of solid materialphases through a segmentation process;

c) obtaining a criterion relationship developed independently of thesegmented volume as a function of a pair of criterion properties relatedto the target property;

d) creating an adjusted segmented volume through additional processing,comprising:

-   -   1) determining where to add a plurality of cracks to the        segmented volume, comprising:        -   i) creating an inverse distance map of the pore space to the            solid material phase boundaries in the segmented volume;        -   ii) creating a watershed surface identifying locations for            potentially introducing cracks into the solid material            phases by applying a watershed processing step to said            inverse distance map;        -   iii) selecting potential crack locations as all portions of            the watershed surface located in the solid phases of the            segmented volume;    -   2) selecting a value for degree of volume revision;    -   3) producing a revised segmented volume, comprising:        -   I) selecting a portion of potential crack locations guided            by degree of revision value;        -   II) converting the voxels of the segmented volume which are            located on said selected portion of potential crack            locations from solid phases to pore;    -   4) deriving the values of criterion properties from the analysis        of the revised segmented volume;    -   5) repeating at least the steps 3 through 4 (or steps 2        through 4) by varying the selected degree of volume revision        until the values of said criterion properties derived in step 4        satisfy the criterion relationship;    -   6) selecting the revised segmented volume which produced the set        of criterion properties which satisfy the criterion relationship        best, as the adjusted segmented volume; and

e) using the adjusted segmented volume to derive the target propertyvalue.

-   11. The method of any preceding or following    embodiment/feature/aspect, wherein obtaining the three-dimensional    tomographic digital image of the sample comprises using at least one    of a group comprising: a focused ion beam scanning electron    microscope, X-ray computed tomography, and magnetic resonance    imaging.-   12. The method of any preceding or following    embodiment/feature/aspect, wherein the target property value    comprises a value selected from a group of properties comprising:    absolute permeability, relative permeability, capillary pressure,    electrical resistivity and select elastic properties; and    wherein the porous material sample is a rock sample.-   13. The method of any preceding or following    embodiment/feature/aspect, wherein:

a) the target property comprises a value selected from a groupcomprising: absolute permeability, relative permeability, capillarypressure, and electrical resistivity; and

b) the pair of criterion properties are a select elastic property andporosity.

-   14. The method of any preceding or following    embodiment/feature/aspect, wherein the select elastic property is an    elastic wave velocity V_(P).-   15. The method of any preceding or following    embodiment/feature/aspect, wherein obtaining the criterion    relationship independent of the digital volume comprises one or more    of a group comprising: calculating a theoretical criterion    relationship based on a theoretical rock physics model, employing an    empirical velocity-porosity transform, and deriving a relationship    from a number of data points relevant to the rock sample.-   16. The method of any preceding or following    embodiment/feature/aspect, wherein deriving the values of selected    elastic property utilizes replacing all mineral phases in adjusted    segmented volume by one selected mineral, for which the criterion    relation can be obtained.-   17. The method of any preceding or following    embodiment/feature/aspect, wherein the selected mineral is one of    quartz, calcite, or dolomite.-   18. The method of any preceding or following    embodiment/feature/aspect, further comprising:

a) obtaining, after step c) and before step d), characteristicgrey-scale value of the voxels of the grey-scale volume located in thepore space of the said segmented volume; and

b) wherein (1) the selecting of a degree of volume revision comprisesselecting a grey-scale value larger than said characteristic grey-scalevalue of the pore space; and (2) the selecting of a portion of potentialcrack locations guided by degree of revision value comprises selectingthose voxels of potential crack locations, whose grey-scale value in thegrey-scale volume is smaller than the degree of volume revision

-   19. The method of any preceding or following    embodiment/feature/aspect, wherein:

a) the sample of a porous media comprises a rock sample; and

b) the target property is selected from a group comprising: absolutepermeability, relative permeability, capillary pressure, and electricalresistivity.

-   20. A method for increasing the accuracy of a target property value    derived from a digital image representing a rock sample, comprising:

a) obtaining a grey-scale digital volume of the rock sample;

b) obtaining a preliminary segmented volume of the rock sample byprocessing the grey-scale volume to a plurality of pore spaces and atleast one solid material phase separated through a segmentation process;

c) defining a criterion curve developed independently of the preliminarysegmented volume as a function of a pair of criterion properties relatedto the target property;

d) creating an adjusted segmented volume through additional processing,comprising:

-   -   1) determining where to add a plurality of cracks to the        preliminary segmented volume, comprising:        -   i) creating an inverse distance map of the pore space to the            solid material phase boundaries in the preliminary segmented            volume;        -   ii) applying a processing step identifying locations for            potentially introducing cracks into the solid material phase            as a function of the inverse distance map;    -   2) introducing cracks to the preliminary segmented volume until        the adjusted segmented volume associated with values for the        pair of criterion properties that satisfies the criterion curve        to produce an adjusted segmented volume;

e) producing and storing an improved segmented volume incorporating thecracks realized in the identified adjusted segmented volume; and

f) using the improved segmented volume to derive a final value for thetarget property.

-   21. The method of any preceding or following    embodiment/feature/aspect, wherein absolute permeability is the    target property and wherein the identified adjusted segmented volume    is the improved segmented volume.-   22. The method of any preceding or following    embodiment/feature/aspect, wherein the target property is related to    pore space connectivity and obtaining a grey-scale image of the rock    sample comprises scanning the rock sample under circumstances in    which resolution available in an initial digital image is    insufficient to effectively directly capture data accurately    representing total pore space connectivity.-   23. The method of any preceding or following    embodiment/feature/aspect, wherein determining the degree to which    cracks are to be realized further comprises:

a) selecting an initial grey-scale watershed cut-off for reallocatingpore space in the revised segmented volume higher than present in therock sample,

b) incrementally adjusting the grey-scale watershed cut-off forreallocating pore space wherein the adjusting proceeds incrementallyfrom low to high.

-   24. The method of any preceding or following    embodiment/feature/aspect, further comprising deriving a preliminary    value from the preliminary segmented volume and comparing the    preliminary target value with expectations developed independent of    the preliminary segmented volume.-   25. A method for developing an adjusted absolute permeability value    from a segmented volume created from tomographic image data obtained    at a resolution insufficient to effectively resolve pore space    connectivity directly from a rock sample under investigation, said    method comprising:

a) obtaining a segmented volume representing the rock sample segmentedto pore spaces and solid material phase, comprising:

-   -   1) scanning the rock sample to produce a grey-scale image; and    -   2) segmenting the grey-scale image to produce a segmented volume        composed of voxels representing pore space and voxels        representing at least one solid material phase;

b) obtaining a grey-scale value characterizing pore space;

c) obtaining a grey-scale value characterizing solid material;

d) defining a criterion curve developed independently of the segmentedvolume as a function of a select elastic property and porosity;

e) creating an inverse distance map of the pore space to the solidmaterial phase boundary from the segmented volume;

f) creating a watershed surface by applying a watershed process to theinverse distance map to identify potential locations for introducingcracks;

g) producing a revised segmented volume based upon a given degree ofrevision; comprising:

-   -   1) selecting a watershed grey-scale cut-off value;    -   2) finding all voxels in the grey-scale digital volume which        have their grey-scale value between the grey-scale value of the        pores and the watershed cut-off value;    -   3) finding among those voxels the voxels co-located with        potential locations for introducing cracks identified by the        watershed process; and    -   4) converting the corresponding voxels of the segmented volume        to voxels representing pore space;

h) deriving trial values for the select elastic property and porosityfrom an analysis of the revised segmented volume;

i) comparing the trial values for the select elastic property andporosity with the criterion curve, adjusting the grey-scale watershedcut-off for reallocating pore space and iteratively repeating stepse)-i) until trial values satisfy the criterion curve and beforeproceeding to step j;

j) producing, and optionally storing for use in further digital rockphysics applications, an improved segmented volume incorporating thecracks of the adjusted segmented volume; and

k) using the improved segmented volume to derive the final absolutepermeability value.

-   26. The method of any preceding or following    embodiment/feature/aspect, wherein obtaining the grey-scale image of    the rock sample comprises using one or more from a group comprising:    focused ion beam scanning electron microscope, X-ray computed    tomography, and magnetic resonance imaging.-   27. The method of any preceding or following    embodiment/feature/aspect, wherein defining the criterion curve    independent of the digital volume comprises one or more from a group    comprising: calculating a theoretical criterion curve based on a    theoretical rock physics model, employing an empirical    velocity-porosity transform, and deriving a curve from a number of    data points relevant to the rock sample.-   28. The method of any preceding or following    embodiment/feature/aspect, wherein defining the criterion curve    independent of the segmented volume further comprises an analysis    based on an assumption that all that is not pore is a single pure    mineral and wherein the step of deriving trial values from the    digital volume applies the same assumption and mineral.-   29. The method of any preceding or following    embodiment/feature/aspect, wherein selecting an initial grey-scale    watershed cut-off for reallocating pore space comprises selecting a    grey-scale watershed cut-off for producing pore space in the revised    segmented volume higher than grey-scale value characterizing the    pore space, and wherein incrementally adjusting the grey-scale    watershed cut-off thereafter for reallocating pore space comprises    bracketing with a low value and incrementally increasing the    grey-scale watershed cut-off.-   30. The method of any preceding or following    embodiment/feature/aspect, wherein using the segmented volume    associated with the trial values satisfying the criterion curves to    derive the adjusted absolute permeability value further comprises    deriving the final absolute permeability values in all three    directions of the segmented volume.-   31. A method for increasing the accuracy with which a segmented    volume represents a material sample having sub-resolution structure,    comprising:

a) obtaining a grey-scale 3-D digital image of the sample;

b) obtaining a preliminary segmented volume corresponding to the sampleby processing the grey-scale image through a segmentation process;

c) defining a criterion relation developed independently of thesegmented volume as a function of a pair of criterion properties relatedto a target property;

d) creating an adjusted segmented volume through additional processing,comprising:

-   -   1) applying a processing step identifying locations for        potentially revising structural features of the segmented        volume; and    -   2) determining the degree to which revisions to structural        features are to be realized in revising the segmented volume by        identifying the adjusted segmented volume associated with values        for the pair of criterion properties that satisfies the        criterion relation; and

e) storing the revised structural features of the identified adjustedsegmented volume for use in further digital rock physics applications.

-   32. The method of any preceding or following    embodiment/feature/aspect, wherein obtaining a grey-scale image of    the sample comprises scanning the sample with at least one of the    following: focused ion beam scanning electron microscope, X-ray    computed tomography, and magnetic resonance imaging.-   33. The method of any preceding or following    embodiment/feature/aspect, wherein obtaining a segmented volume    corresponding to the sample by processing the grey-scale image to a    plurality of phases comprises producing the segmented volume    composed of voxels characterized as either pore space or solid    material phase.-   34. The method of any preceding or following    embodiment/feature/aspect, wherein the material sample is rock and    wherein:

a) revising features comprises adding cracks;

b) applying a watershed processing step identifying locations forpotentially revising features of the segmented volume further comprises:

-   -   1) creating an inverse distance map of the pore space to the        solid material phase boundaries in the segmented volume; and    -   2) applying a processing step for identifying positions for        potentially introducing cracks into the solid material phase as        a function of the inverse distance map; and

c) defining a criterion relation developed independently of thesegmented volume as a function of a pair of criterion properties relatedto the target property further comprises:

-   -   1) expressing the criterion relation as a criterion curve; and    -   2) defining the criterion curve, comprises using one or more of        a group comprising: calculating a theoretical criterion curve        based on a theoretical rock physics model, employing an        empirical transform, or deriving a relationship from a number of        data points relevant to the rock sample;

d) determining the degree to which features are to be realized inrevising the segmented volume by identifying an adjusted segmentedvolume associated with values for the pair of criterion properties thatsatisfies the criterion relation further comprises:

-   -   1) obtaining characteristic grey-scale value of the pore space    -   2) applying an iterative watershed cut-off value; comprising:        -   i) finding all voxels in the grey-scale image which have            their grey-scale value between the characteristic grey-scale            value of the pores and the iterative watershed cut-off            value;        -   ii) finding among those voxels the voxels co-located with            potential locations for introducing cracks identified in the            watershed surface;        -   iii) converting the corresponding voxels of the segmented            volume to voxels representing pore space;        -   iv) deriving trial values for the select elastic property            and porosity from an analysis of the revised segmented            volume; and        -   v) comparing the trial values for the select elastic            property and porosity with the criterion curve, adjusting            the grey-scale watershed cut-off for reallocating pore space            and iteratively repeating steps d)(2)i)-d)(2)v) until the            trial values satisfy the criterion curve.

-   35. The method of any preceding or following    embodiment/feature/aspect, wherein the pair of criterion properties    comprise porosity and a select elastic property.

-   36. The method of any preceding or following    embodiment/feature/aspect, further comprising using the revised    structural features of the identified adjusted segmented volume to    derive a value for the target property which is selected from a    group of properties comprising: absolute permeability, relative    permeability, capillary pressure, and electrical resistivity.

-   37. The method of any preceding or following    embodiment/feature/aspect, further comprising using the revised    structural features of the identified adjusted segmented volume to    derive a value for at least one other the fluid flow property.

-   38. The method of any preceding or following    embodiment/feature/aspect, further comprising combining the revised    structural features of the identified adjusted segmented image with    data from at least one other segmented image.

-   39. The method of any preceding or following    embodiment/feature/aspect, wherein at least one of the other    segmented images with which the revised structural features are    combined has a plurality of solid material phases.

-   40. A system for increasing the accuracy of a target property value    derived from a digital image corresponding to a material sample,    comprising:

a) an X-ray scanner operable to scan a rock sample to obtain athree-dimensional tomographic digital image, such as a 2D grey-scaleimage, of the rock sample; and

b) one or more computer systems operable to i) obtain athree-dimensional tomographic digital image, such as a grey-scale 3-Ddigital image, of the material sample; ii) obtain a preliminarysegmented volume corresponding to the material sample by processing thegrey-scale 3D digital image through a segmentation process; iii) createa criterion relation developed independently of the preliminarysegmented volume as a function of criterion property values related tothe target property; iv) create an adjusted segmented volume throughadditional revising features to the preliminary segmented volume,comprising: 1) apply a processing step to identify locations forpotentially revising features of the preliminary segmented volume; 2)apply revision features to the preliminary segmented volume to create arevised segmented volume; 3) derive trial values of criteria propertiesfrom the revised segmented volume; 4) repeat at least steps 2)-3) on therevised segmented volume until trial values of criterion propertiessatisfy the criterion relation; v) store an adjusted segmented volumeincorporating the revised features of the adjusted segmented volumeidentified; vi) derive a final value for the target property from theadjusted segmented volume; and vii) output the results to at least onedevice to display, print, or store results of the computations; and

c) at least one device to display, print, or store results of thecomputations.

-   41. A computer program product on a non-transitory computer readable    medium that, when performed on a processor in a computerized device    provides a method for performing computations of one or more or all    of the indicated steps of the method of any preceding claim.-   42. A segmented digital volume representing a sample of a porous    media comprising:

a) voxels representing pore space derived from segmentation of a 3D greyscale digital image;

b) voxels representing at least one solid material phase derived fromsegmentation of the 3D grey scale digital image; and

c) converted voxels representing structural features not fully resolvedin the 3D grey scale digital image or the direct segmentation thereofwherein:

the placement of the converted voxels is derived from additionalprocessing steps using data from the 3D grey-scale digital image and oneor more segmented volumes derived therefrom; and

the volume of converted voxels in place is solved to satisfy a criteriarelation representative of the sample and independent of the 3Dgrey-scale image.

-   43. A segmented digital volume of any preceding or following    embodiment/feature/aspect, wherein:

the structural features are cracks unresolved in the 3D grey-scale imageand contributing pore space connectivity present in the porous media notaccounted for in a preliminary segmentation of the 3D grey-scale image;and

the converted voxels represent additional pore space.

-   44. A segmented digital volume of any preceding or following    embodiment/feature/aspect, wherein:

the structural features are conduits unresolved in the 3D grey-scaleimage and contributing pore space connectivity present in the porousmedia not accounted for in a preliminary segmentation of the 3Dgrey-scale image; and

the converted voxels represent additional pore space.

The present invention can include any combination of these variousfeatures or embodiments above and/or below as set forth in sentencesand/or paragraphs. Any combination of disclosed features herein isconsidered part of the present invention and no limitation is intendedwith respect to combinable features.

Applicants specifically incorporate the entire contents of all citedreferences in this disclosure.

Other embodiments of the present invention will be apparent to thoseskilled in the art from consideration of the present specification andpractice of the present invention disclosed herein. It is intended thatthe present specification and examples be considered as exemplary onlywith a true scope and spirit of the invention being indicated by thefollowing claims and equivalents thereof.

What is claimed is:
 1. A method for increasing the accuracy of a targetproperty value derived from a digital image representing a materialsample, comprising: a) obtaining a three-dimensional tomographic digitalimage of the material sample; b) generating a preliminary segmentedvolume corresponding to the material sample by processing thethree-dimensional tomographic digital image through a segmentationprocess; c) obtaining a criterion relation developed independently ofthe preliminary segmented volume as a function of values of criterionproperties related to the target property; d) creating an adjustedsegmented volume through additional revising features to the preliminarysegmented volume, comprising: 1) applying a processing step to identifylocations for potentially revising features of the preliminary segmentedvolume; 2) applying revision features to the preliminary segmentedvolume to create a revised segmented volume; 3) deriving trial values ofcriteria properties from the revised segmented volume; 4) repeating atleast steps 2)-3) on the revised segmented volume until trial values ofcriterion properties satisfy the criterion relation; and e) deriving afinal value for the target property from the adjusted segmented volume.2. The method of claim 1, wherein the values of criterion properties arevalues of a pair of criterion properties.
 3. The method of claim 1,wherein the obtaining a three-dimensional tomographic digital image ofthe material sample comprises scanning the material sample with at leastone of a group comprising: focused ion beam scanning electronmicroscope, X-ray computed tomography, and magnetic resonance imaging.4. The method of claim 1, wherein the obtaining of the preliminarysegmented volume corresponding to the material sample comprisesprocessing the three-dimensional tomographic digital image to aplurality of phases for producing the preliminary segmented volume ascomprised of voxels characterized as either pore space or solid materialphase.
 5. The method of claim 1, wherein: a) the revising of featurescomprises adding cracks; b) the applying of a processing step toidentify locations for potentially revising features of the preliminarysegmented volume further comprises: 1) creating an inverse distance mapof the pore space to the solid material phase boundaries in thepreliminary segmented volume; and 2) applying a watershed processingstep for identifying positions for potentially introducing cracks intothe solid material phase as a function of the inverse distance map; andc) the obtaining of a criterion relation developed independently of thepreliminary segmented volume as a function of a pair of criterionproperties related to the target property further comprises defining thecriterion relationship using one or more of a group comprising:calculating a theoretical criterion relationship based on a theoreticalmaterial physics model, employing an empirical transform, and deriving arelationship from a number of data points relevant to the materialsample; d) the creating of an adjusted segmented volume throughadditional revising features to the preliminary segmented volume furthercomprises revising the adjusted segmented volume until the associatedvalues for the pair of criterion properties satisfies the criterionrelation, and further comprises: (1) obtaining a characteristicgrey-scale value of the pore space, (2) applying an iterative watershedcut-off value; comprising: i) selecting a watershed grey-scale cut-offvalue; ii) finding all candidate voxels in the three-dimensionaltomographic digital image which have their grey-scale value between thecharacteristic grey-scale value of the pore space and the iterativewatershed cut-off value; iii) finding among those candidate voxels thevoxels to be realized which are co-located with potential locations forintroducing cracks identified in the watershed surface; and iv)converting the voxels identified to be realized in the segmented volumeto voxels representing pore space; v) deriving trial values forcriterion properties from an analysis of the revised segmented volume;and vi) comparing the trial values for the criterion properties with thecriterion relationship, adjusting the grey-scale watershed cut-off forreallocating pore space and iteratively repeating steps ii) to vi) untilthe trial values satisfy the criterion relationship.
 6. The method ofclaim 2, wherein: a) the material sample comprises a rock sample; b) thepair of criterion properties comprise porosity and a select elasticproperty; and c) the target property is selected from a groupcomprising: absolute permeability, relative permeability, capillarypressure, and electrical resistivity.
 7. The method for increasing theaccuracy of the target property value in accordance with claim 1 furthercomprising populating the adjusted segmented volume with additionalproperties, and using a resulting segmented volume to derive additionalproperties of interest from the adjusted segmented volume.
 8. The methodof claim 1, wherein step 4) comprises repeating steps 1)-3) on therevised segmented volume until trial values of criterion propertiessatisfy the criterion relation.
 9. The method of claim 1, furthercomprising storing the adjusted segmented volume created in step d). 10.A method for increasing the accuracy of a target property value derivedfrom a digital image representing a porous material sample, comprising:a) obtaining a three-dimensional tomographic digital image comprising agrey-scale volume of the sample; b) obtaining a segmented volumerepresenting the sample by processing the grey-scale volume to porespace and a plurality of solid material phases through a segmentationprocess; c) obtaining a criterion relationship developed independentlyof the segmented volume as a function of a pair of criterion propertiesrelated to the target property; d) creating an adjusted segmented volumethrough additional processing, comprising: 1) determining where to add aplurality of cracks to the segmented volume, comprising: i) creating aninverse distance map of the pore space to the solid material phaseboundaries in the segmented volume; ii) creating a watershed surfaceidentifying locations for potentially introducing cracks into the solidmaterial phases by applying a watershed processing step to said inversedistance map; iii) selecting potential crack locations as all portionsof the watershed surface located in the solid phases of the segmentedvolume; 2) selecting a value for degree of volume revision; 3) producinga revised segmented volume, comprising: I) selecting a portion ofpotential crack locations guided by degree of revision value; II)converting the voxels of the segmented volume which are located on saidselected portion of potential crack locations from solid phases to pore;4) deriving the values of criterion properties from the analysis of therevised segmented volume; 5) repeating at least the steps 3 through 4 byvarying the selected degree of volume revision until the values of saidcriterion properties derived in step 4 satisfy the criterionrelationship; 6) selecting the revised segmented volume which producedthe set of criterion properties which satisfy the criterion relationshipbest, as the adjusted segmented volume; and e) using the adjustedsegmented volume to derive the target property value.
 11. The method ofclaim 10, wherein obtaining the three-dimensional tomographic digitalimage of the sample comprises using at least one of a group comprising:a focused ion beam scanning electron microscope, X-ray computedtomography, and magnetic resonance imaging.
 12. The method of claim 10,wherein the target property value comprises a value selected from agroup of properties comprising: absolute permeability, relativepermeability, capillary pressure, electrical resistivity and selectelastic properties; and wherein the porous material sample is a rocksample.
 13. The method of claim 10, wherein: a) the target propertycomprises a value selected from a group comprising: absolutepermeability, relative permeability, capillary pressure, and electricalresistivity; and b) the pair of criterion properties are a selectelastic property and porosity.
 14. The method of claim 13, wherein theselect elastic property is an elastic wave velocity V_(p).
 15. Themethod of claim 13, wherein obtaining the criterion relationshipindependent of the digital volume comprises one or more of a groupcomprising: calculating a theoretical criterion relationship based on atheoretical rock physics model, employing an empirical velocity-porositytransform, and deriving a relationship from a number of data pointsrelevant to the rock sample.
 16. The method of claim 13, whereinderiving the values of selected elastic property utilizes replacing allmineral phases in adjusted segmented volume by one selected mineral, forwhich the criterion relation can be obtained.
 17. The method of claim16, wherein the selected mineral is one of quartz, calcite, or dolomite.18. The method of claim 10, further comprising: a) obtaining, after stepc) and before step d), characteristic grey-scale value of the voxels ofthe grey-scale volume located in the pore space of the said segmentedvolume; and b) wherein (1) the selecting of a degree of volume revisioncomprises selecting a grey-scale value larger than said characteristicgrey-scale value of the pore space; and (2) the selecting of a portionof potential crack locations guided by degree of revision valuecomprises selecting those voxels of potential crack locations, whosegrey-scale value in the grey-scale volume is smaller than the degree ofvolume revision
 19. The method of claim 10, wherein: a) the sample of aporous media comprises a rock sample; and b) the target property isselected from a group comprising: absolute permeability, relativepermeability, capillary pressure, and electrical resistivity.
 20. Amethod for increasing the accuracy of a target property value derivedfrom a digital image representing a rock sample, comprising: a)obtaining a grey-scale digital volume of the rock sample; b) obtaining apreliminary segmented volume of the rock sample by processing thegrey-scale volume to a plurality of pore spaces and at least one solidmaterial phase separated through a segmentation process; c) defining acriterion curve developed independently of the preliminary segmentedvolume as a function of a pair of criterion properties related to thetarget property; d) creating an adjusted segmented volume throughadditional processing, comprising: 1) determining where to add aplurality of cracks to the preliminary segmented volume, comprising: i)creating an inverse distance map of the pore space to the solid materialphase boundaries in the preliminary segmented volume; ii) applying aprocessing step identifying locations for potentially introducing cracksinto the solid material phase as a function of the inverse distance map;2) introducing cracks to the preliminary segmented volume until theadjusted segmented volume associated with values for the pair ofcriterion properties that satisfies the criterion curve to produce anadjusted segmented volume; e) producing and storing an improvedsegmented volume incorporating the cracks realized in the identifiedadjusted segmented volume; and f) using the improved segmented volume toderive a final value for the target property.
 21. The method of claim20, wherein absolute permeability is the target property and wherein theidentified adjusted segmented volume is the improved segmented volume.22. The method of claim 20, wherein the target property is related topore space connectivity and obtaining a grey-scale image of the rocksample comprises scanning the rock sample under circumstances in whichresolution available in an initial digital image is insufficient toeffectively directly capture data accurately representing total porespace connectivity.
 23. The method of claim 20, wherein determining thedegree to which cracks are to be realized further comprises: a)selecting an initial grey-scale watershed cut-off for reallocating porespace in the revised segmented volume higher than present in the rocksample, b) incrementally adjusting the grey-scale watershed cut-off forreallocating pore space wherein the adjusting proceeds incrementallyfrom low to high.
 24. The method of claim 20, further comprisingderiving a preliminary value from the preliminary segmented volume andcomparing the preliminary target value with expectations developedindependent of the preliminary segmented volume.
 25. A method fordeveloping an adjusted absolute permeability value from a segmentedvolume created from tomographic image data obtained at a resolutioninsufficient to effectively resolve pore space connectivity directlyfrom a rock sample under investigation, said method comprising: a)obtaining a segmented volume representing the rock sample segmented topore spaces and solid material phase, comprising: 1) scanning the rocksample to produce a grey-scale image; and 2) segmenting the grey-scaleimage to produce a segmented volume composed of voxels representing porespace and voxels representing at least one solid material phase; b)obtaining a grey-scale value characterizing pore space; c) obtaining agrey-scale value characterizing solid material; d) defining a criterioncurve developed independently of the segmented volume as a function of aselect elastic property and porosity; e) creating an inverse distancemap of the pore space to the solid material phase boundary from thesegmented volume; f) creating a watershed surface by applying awatershed process to the inverse distance map to identify potentiallocations for introducing cracks; g) producing a revised segmentedvolume based upon a given degree of revision; comprising: 1) selecting awatershed grey-scale cut-off value; 2) finding all voxels in thegrey-scale digital volume which have their grey-scale value between thegrey-scale value of the pores and the watershed cut-off value; 3)finding among those voxels the voxels co-located with potentiallocations for introducing cracks identified by the watershed process;and 4) converting the corresponding voxels of the segmented volume tovoxels representing pore space; h) deriving trial values for the selectelastic property and porosity from an analysis of the revised segmentedvolume; i) comparing the trial values for the select elastic propertyand porosity with the criterion curve, adjusting the grey-scalewatershed cut-off for reallocating pore space and iteratively repeatingsteps e)-i) until trial values satisfy the criterion curve and beforeproceeding to step j; j) producing and storing an improved segmentedvolume incorporating the cracks of the adjusted segmented volume; and k)using the improved segmented volume to derive the final absolutepermeability value.
 26. The method of claim 25, wherein obtaining thegrey-scale image of the rock sample comprises using one or more from agroup comprising: focused ion beam scanning electron microscope, X-raycomputed tomography, and magnetic resonance imaging.
 27. The method ofclaim 26, wherein defining the criterion curve independent of thedigital volume comprises one or more from a group comprising:calculating a theoretical criterion curve based on a theoretical rockphysics model, employing an empirical velocity-porosity transform, andderiving a curve from a number of data points relevant to the rocksample.
 28. The method of claim 27, wherein defining the criterion curveindependent of the segmented volume further comprises an analysis basedon an assumption that all that is not pore is a single pure mineral andwherein the step of deriving trial values from the digital volumeapplies the same assumption and mineral.
 29. The method of claim 28,wherein selecting an initial grey-scale watershed cut-off forreallocating pore space comprises selecting a grey-scale watershedcut-off for producing pore space in the revised segmented volume higherthan grey-scale value characterizing the pore space, and whereinincrementally adjusting the grey-scale watershed cut-off thereafter forreallocating pore space comprises bracketing with a low value andincrementally increasing the grey-scale watershed cut-off.
 30. Themethod of claim 29, wherein using the segmented volume associated withthe trial values satisfying the criterion curves to derive the adjustedabsolute permeability value further comprises deriving the finalabsolute permeability values in all three directions of the segmentedvolume.
 31. A method for increasing the accuracy with which a segmentedvolume represents a material sample having sub-resolution structure,comprising: a) obtaining a grey-scale 3-D digital image of the sample;b) obtaining a preliminary segmented volume corresponding to the sampleby processing the grey-scale image through a segmentation process; c)defining a criterion relation developed independently of the segmentedvolume as a function of a pair of criterion properties related to atarget property; d) creating an adjusted segmented volume throughadditional processing, comprising: 1) applying a processing stepidentifying locations for potentially revising structural features ofthe segmented volume; and 2) determining the degree to which revisionsto structural features are to be realized in revising the segmentedvolume by identifying the adjusted segmented volume associated withvalues for the pair of criterion properties that satisfies the criterionrelation; and e) storing the revised structural features of theidentified adjusted segmented volume for use in further digital rockphysics applications.
 32. The method of claim 31, wherein obtaining agrey-scale image of the sample comprises scanning the sample with atleast one of the following: focused ion beam scanning electronmicroscope, X-ray computed tomography, and magnetic resonance imaging.33. The method of claim 32, wherein obtaining a segmented volumecorresponding to the sample by processing the grey-scale image to aplurality of phases comprises producing the segmented volume composed ofvoxels characterized as either pore space or solid material phase. 34.The method of claim 33, wherein the material sample is rock and wherein:a) revising features comprises adding cracks; b) applying a watershedprocessing step identifying locations for potentially revising featuresof the segmented volume further comprises: 1) creating an inversedistance map of the pore space to the solid material phase boundaries inthe segmented volume; and 2) applying a processing step for identifyingpositions for potentially introducing cracks into the solid materialphase as a function of the inverse distance map; and c) defining acriterion relation developed independently of the segmented volume as afunction of a pair of criterion properties related to the targetproperty further comprises: 1) expressing the criterion relation as acriterion curve; and 2) defining the criterion curve, comprises usingone or more of a group comprising: calculating a theoretical criterioncurve based on a theoretical rock physics model, employing an empiricaltransform, or deriving a relationship from a number of data pointsrelevant to the rock sample; d) determining the degree to which featuresare to be realized in revising the segmented volume by identifying anadjusted segmented volume associated with values for the pair ofcriterion properties that satisfies the criterion relation furthercomprises: 1) obtaining characteristic grey-scale value of the porespace (2) applying an iterative watershed cut-off value; comprising: i)finding all voxels in the grey-scale image which have their grey-scalevalue between the characteristic grey-scale value of the pores and theiterative watershed cut-off value; ii) finding among those voxels thevoxels co-located with potential locations for introducing cracksidentified in the watershed surface; iii) converting the correspondingvoxels of the segmented volume to voxels representing pore space; iv)deriving trial values for the select elastic property and porosity froman analysis of the revised segmented volume; and v) comparing the trialvalues for the select elastic property and porosity with the criterioncurve, adjusting the grey-scale watershed cut-off for reallocating porespace and iteratively repeating steps d)(2)i) to d)(2)v) until the trialvalues satisfy the criterion curve.
 35. The method of claim 34, whereinthe pair of criterion properties comprise porosity and a select elasticproperty.
 36. The method of claim 35, further comprising using therevised structural features of the identified adjusted segmented volumeto derive a value for the target property which is selected from a groupof properties comprising: absolute permeability, relative permeability,capillary pressure, and electrical resistivity.
 37. The method of claim36, further comprising using the revised structural features of theidentified adjusted segmented volume to derive a value for at least oneother the fluid flow property.
 38. The method of claim 37, furthercomprising combining the revised structural features of the identifiedadjusted segmented image with data from at least one other segmentedimage.
 39. The method of claim 38, wherein at least one of the othersegmented images with which the revised structural features are combinedhas a plurality of solid material phases.
 40. A system for increasingthe accuracy of a target property value derived from a digital imagecorresponding to a material sample, comprising: a) an X-ray scanneroperable to scan a rock sample to obtain a three-dimensional tomographicdigital image of the rock sample; and b) one or more computer systemsoperable to i) obtain a three-dimensional tomographic digital image ofthe material sample; ii) generate a preliminary segmented volumecorresponding to the material sample by processing the three-dimensionaltomographic digital image through a segmentation process; iii) obtain acriterion relation developed independently of the preliminary segmentedvolume as a function of values of criterion properties related to thetarget property; iv) create an adjusted segmented volume throughadditional revising features to the preliminary segmented volume,comprising: 1) apply a processing step to identify locations forpotentially revising features of the preliminary segmented volume; 2)apply revision features to the preliminary segmented volume to create arevised segmented volume; 3) derive trial values of criteria propertiesfrom the revised segmented volume; 4) repeat at least steps 2)-3) on therevised segmented volume until trial values of criterion propertiessatisfy the criterion relation; v) store an adjusted segmented volumeincorporating the revised features of the adjusted segmented volumeidentified; vi) derive a final value for the target property from theadjusted improved segmented volume; and vii) output the results to atleast one device to display, print, or store results of thecomputations; and c) at least one device to display, print, or storeresults of the computations.
 41. A computer program product on anon-transitory computer readable medium that, when performed on aprocessor in a computerized device provides a method for performingcomputations of one or more or all of the indicated steps of the methodof claim 1.